Feynman Path Integrals Over Entangled States

Green, A. G.; Hooley, C. A.; Keeling, J.; Simon, S. H.

doi:10.48550/arxiv.1607.01778

Cited by 12 publications

(19 citation statements)

References 35 publications

(54 reference statements)

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“…2, 3 is the MPS tensor. A tensor of bond order D and local Hilbert space dimension D is represented by an SU (dD) matrix following [13,[33][34][35][36] A σ ij = U (1⊗j),(σ⊗i) as shown in Fig. 6.…”

Section: Acknowledgements and Contributionsmentioning

confidence: 99%

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Parallel quantum simulation of large systems on small NISQ computers

Barratt

Dborin

Bal³

et al. 2021

npj Quantum Inf

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Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.

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Section: Acknowledgements and Contributionsmentioning

confidence: 99%

“…Canonicalisation at each step in a classical tensor network calculation amounts to reducing the tensors to isometries -a step that is not required in an explicitly unitary realisation. Moreover, the remaining elements of unitaries parametrise the tangent space of the variational manifold [12,13].…”

Section: Introductionmentioning

confidence: 99%

Parallel quantum simulation of large systems on small NISQ computers

Barratt

Dborin

Bal³

et al. 2021

npj Quantum Inf

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“…Notice that we will not need to use any non-classical paths or histories; only eight histories need to be considered to get the proper answers. 5 The reason that there are eight histories is as follows: since the two photons are emitted in opposite directions (initially travelling along the solid lined paths or the dashed lined paths), there are only two initial possibilities, with amplitudes A and B for the solid and the dashed lines respectively. For each of these two cases, the photons must either transmit or reflect off a beamsplitter, ending at one detector in each device.…”

Section: Path Integral Calculationsmentioning

confidence: 99%

“…Because a single entangled state has no spatial representation, any of these "paths" would also have no possible spacetime representation. Approaches using such Hilbert space "paths" are common in the literature [3,4], and have even been extended to quantum field theory [5].…”

Section: Introductionmentioning

confidence: 99%

Spacetime Path Integrals for Entangled States

Tyagi,

Wharton

2021

Preprint

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Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of entangled states as entities in a high-dimensional Hilbert space, or the intuitive view of these states as a connection between distant spatial configurations, it may not even be obvious that a pathbased calculation can be achieved using only paths in ordinary space and time. Previous work has shown how to do this for certain special states; this paper extends those results to all pure two-qubit states, where each qubit can be measured in an arbitrary basis. Certain three-qubit states are also developed, and path integrals again reproduce the usual correlations. These results should allow for a substantial amount of conventional quantum analysis to be translated over into a path-integral perspective, simplifying certain calculations, and more generally informing research in quantum foundations.

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“…Our approach remedies this issue because we integrate over Hilbert space which includes entangled states. An attempt to use paths in Hilbert space instead was previously proposed in [2], and a space-time based solution was recently discussed in [3]. Third, it is an example of a future-input-dependent formalism [4] and is hence a starting point to solve the measurement problem, as laid out in [5,6].…”

Section: Introductionmentioning

confidence: 99%

A Future-Input Dependent Path Integral for Quantum Mechanics

Donadi,

Hossenfelder

2021

Preprint

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We here put forward a new path-integral over Hilbert space and show that it reproduces quantum mechanics exactly. This approach works by optimizing the generating functional under a variation of the final state; it is hence an example of a future-input dependent theory. The benefit of this method is that entangled states appear in the paths directly, and the generating functional can be modified to also include wave-function collapse.

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Feynman Path Integrals Over Entangled States

Cited by 12 publications

References 35 publications

Parallel quantum simulation of large systems on small NISQ computers

Parallel quantum simulation of large systems on small NISQ computers

Spacetime Path Integrals for Entangled States

A Future-Input Dependent Path Integral for Quantum Mechanics

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